The generator matrix 1 0 0 1 1 1 X^2+X 1 X^2 1 X 1 1 X^2 1 1 X 1 0 1 X^2 X X^2 1 1 X^2 1 1 X 1 1 1 1 1 0 1 X^2 X^2+X X^2+X 1 0 1 1 1 1 1 X 1 1 X 1 1 X^2+X X^2 X^2 X 1 X^2 1 1 1 0 1 X X 1 X^2+X X^2+X 1 1 1 0 1 0 1 0 1 1 X 1 X 1 X+1 1 X X+1 X+1 0 X^2+X 1 0 1 X^2+X 1 1 X^2+X+1 1 0 X X^2+X X+1 X^2+X X^2+X+1 X^2 X^2 1 X^2+X+1 1 1 X^2+X 0 X 1 1 X X^2+1 X 1 X X^2+1 1 X+1 X 0 1 1 1 X+1 1 X^2+1 X^2 X^2+1 1 X+1 1 1 X^2 1 1 X^2+X+1 X+1 0 0 0 1 1 1 0 1 X+1 X X X^2+1 X 1 1 X+1 0 1 X^2+1 X^2+1 X^2+X 0 1 X^2 X^2 1 X^2+X+1 X+1 X^2 1 X^2+X X^2+X+1 X^2+1 X X 1 1 X^2 X^2+1 1 X^2+X 1 1 1 X X^2+X+1 X^2+X+1 X^2+X+1 X^2+X+1 X^2 X+1 X^2+X+1 X^2 1 1 X^2+1 X^2 0 X^2 X^2+1 X^2+1 X^2 X^2+X 1 1 X X^2 X X+1 X^2 X^2 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X^2 X^2 X X X^2+X X^2+X X X^2+X X X X X^2+X X^2+X X X X^2 X^2 X X^2 0 X X^2+X 0 X^2 0 X^2 X^2+X X X^2+X X^2 X^2+X 0 X^2 X X^2+X X^2+X X^2+X X X X^2+X X 0 X^2 X^2+X X 0 X X^2+X X^2 X^2+X X^2 X^2 X X^2+X X X^2 X 0 0 0 0 0 X 0 0 0 X X^2+X X^2+X X^2+X X^2 X X^2+X X^2+X X X 0 0 X^2 X^2 X 0 X^2+X X^2+X 0 X^2+X X^2+X 0 X X^2+X X^2 X^2+X X^2 X^2 0 X^2+X 0 X^2 0 X X X X^2 X^2+X 0 0 X X X^2 X^2 X^2 X^2+X X^2 0 X^2 X^2+X 0 X^2 0 0 X^2 X X^2+X 0 X^2 0 X^2+X 0 0 0 0 0 0 0 X X^2+X X^2+X X^2+X X 0 X^2 0 X X 0 X 0 X^2+X X^2 0 0 X^2+X X X 0 X X^2+X X X^2 X^2+X X^2 X 0 X^2 X X X X X^2+X X^2+X X^2 X^2+X X^2+X X^2 X^2 0 X^2 X X^2 0 X^2 0 X^2+X X X 0 X^2 X X^2 X^2+X 0 X^2 0 X^2 X^2 X X^2+X 0 X^2+X 0 generates a code of length 71 over Z2[X]/(X^3) who´s minimum homogenous weight is 60. Homogenous weight enumerator: w(x)=1x^0+57x^60+146x^61+434x^62+548x^63+1069x^64+1028x^65+1793x^66+1720x^67+2575x^68+2406x^69+3233x^70+2736x^71+3290x^72+2338x^73+2861x^74+1788x^75+1696x^76+958x^77+886x^78+428x^79+341x^80+138x^81+124x^82+68x^83+50x^84+24x^85+10x^86+8x^87+7x^88+2x^90+2x^92+2x^93+1x^94 The gray image is a linear code over GF(2) with n=284, k=15 and d=120. This code was found by Heurico 1.16 in 50.3 seconds.